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 A209834 a(A074773(n) mod 1519829 mod 18) = A074773(n), 1 <= n <= 18. 2

%I #9 Jun 07 2023 11:03:03

%S 3343433905957,1871186716981,307768373641,546348519181,1362242655901,

%T 2273312197621,354864744877,3474749660383,2366338900801,602248359169,

%U 3215031751,2152302898747,315962312077,457453568161,528929554561,3477707481751,118670087467,3461715915661

%N a(A074773(n) mod 1519829 mod 18) = A074773(n), 1 <= n <= 18.

%C From the first reference, for numbers up to 10^12 only four strong pseudoprimality tests (with bases 2, 13, 23, 1662803) are necessary for proving primality. Since A074773(19) = 4341937413061, up to 4.10^12 we can use the four bases 2, 3, 5, 7 and if a number n passes the tests, we check if n is equal to a(n mod 1519829 mod 18). If not, n is prime. A unique comparison is used so we have a primality test equally efficient for an interval four times larger. See the Bomfim link.

%C Terms computed using table by Charles R Greathouse IV. See A074773.

%H Washington Bomfim, <a href="/A209834/a209834.txt">A method to find bijections from a set of n integers to {0,1, ... ,n-1}</a>

%H G. Jaeschke, <a href="http://dx.doi.org/10.1090/S0025-5718-1993-1192971-8">On strong pseudoprimes to several bases</a>, Mathematics of Computation, 61 (1993), 915-926.

%e A074773(15) mod 1519829 mod 18 = 0, so a(0) = A074773(15).

%e A074773(11) mod 1519829 mod 18 = 1, so a(1) = A074773(11).

%Y Cf. A074773, A209833.

%K nonn,fini,full

%O 0,1

%A _Washington Bomfim_, Mar 14 2012

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Last modified June 20 20:49 EDT 2024. Contains 373532 sequences. (Running on oeis4.)